Forum Emoji

I know that the post/comment editor here has a "Smileys" panel for adding emoji via a click or two, but there are also some emoji that are auto-converted from text; e.g. : ) (minus the space) becoming

For some bizarre reason I felt compelled to find a comprehensive list of these latter options, both for myself and everyone else here. After tracking down the name of this forum software (Vanilla), I found this: